Volume 128, Issue 3-6

Wide-angle x-ray diagrams of quartz (Bragg and Laue case) showed along the lines of weak and of missing reflections (forbidden ones) a rather close sequence of “umweganregung” spots. These spots were indexed by a special method. With the crystal surface etched or polished, the form of the spots was as expected. With the surface ground, the spots along the forbidden lines showed double-spikes, their directions varying from spot to spot as well as with the source-to-crystal and crystal-to-film distances. The spikes are considered as a special kind of reflection broadening produced by the mosaic structure of the crystal surface. Each of the two reflections contributing to an umweg reflection consists of two components: the first is rather divergent because it is produced by the mosaic layer formed by grinding; the second is just slightly divergent because it is produced by the crystal matrix which proved to be nearly perfect. The combination of the narrow but intensive component of one reflection with the wide component of the other results in a double-spike. This idealizing concept, mathematically formulated by means of vectors in the reciprocal lattice, quantitatively explained the observed directions of the spikes.

Single-crystal photographs of vaterite ( μ CaCO 3 ) show numerous diffuse streaks ‖ c * with maxima which require an increase in the previous lattice parameter a by a factor [unk]3 to 7.15 Å, and doubling (sometimes trebling) of c to 16.94 Å; moreover satellite reflections were observed. The structure of vaterite can be considered as a disordered stacking sequence of single layers of trigonal symmetry which are mostly related by glide reflections and sometimes by a screw operation ‖ c . Sequences of two layers AA ′ and of four layers AA ′ BB ′ may be considered as states of order which are approached; the partial sequences ABAB and A ′ B ′ A ′ B ′ correspond to the principle of the hexagonal closest packing. For a more exact treatment one has to consider the deformations of the primitive hexagonal partial lattice array of the calcium atoms also. The average structure agrees in general with K amhi's proposal; but the CO 3 group has to be centered around ( j ) of space group P 6 3 / mmc with an occupancy of one sixth only. The least-squares refinement reduced R to 0.115. The oxygen atoms form distorted cubes around the calcium atoms. Conclusions are drawn concerning the structures of rare-earth borates and of the bastnaesite-vaterite series.

The crystal structure of margarosanite with a = 6.768 Å ± .004, b = 9.575 Å ± .004, c = 6.718 Å ± .005, α = 110.36° ± .03, β = 102.98° ± .04, γ = 83.02 ° ± .05, and with space group P [unk] was solved by application of the minimum function to P ( xyz ), and the use of heavy-atom techniques. This procedure yielded a trial structure which was refined by a least-squares method using the full matrix. The unit cell ideally contains 2(PbCa 2 Si 3 O 9 ). The margarosanite structure has the following principle features: 1. planes of tetrahedral sites alternate with planes of calcium sites between sheets of close-packed oxygen atoms parallel to ([unk]01); 2. Pb and Ca are ordered; 3. Ca(1) polyhedra form an infinite edge-sharing chain parallel to [101] and Pb and Ca(2) sites alternate along the edge of this chain; 4. tetrahedral sites form three-membered rings which are linked to the Ca(1) polyhedral chain; and 5. the two Ca atoms have 6-fold coordination and the Pb atom has 7-fold coordination.

The trigonal form of selenourea has been examined by x-ray crystallographic methods both at room temperature and at −100°C. The lattice parameters reported by earlier workers have been refined by least squares to a = 15.285(5) Å, c = 13.007(5) Å at 20°C and a = 15.201(5) Å, c = 12.950(5) Å at −100°C. The space group has been confirmed to be P 3 1 or P 3 2 , which requires nine crystallographically distinct SeC(NH 2 ) 2 molecules. The crystal structure was solved using Patterson techniques and difference Fourier syntheses, and was refined by least squares using three-dimensional data obtained at −100°C. The unit cell contains nine three-fold spiral chains which run parallel to c . The similarity of the crystal structure to the urea- and thiourea-hydrocarbon complexes in discussed. Evidence is presented of N–H⋯Se hydrogen bonds, supporting their recent discovery in chemically related compounds.

A simple optical device is described which makes possible the projection of strongly magnified contours of the crystal (and glass capillary if used). A Fortran-IV program has been written to derive from these contour pictures a net of points representing the surface of the crystal and also the position and diameter of the capillary which is treated as a cylinder. Using this information and a numerical integration method given by H amilton the program then is able to calculate absorption and secondary-extinction corrections for x-ray or neutron-diffraction data. It is shown that the approximation achieved is sufficient for the usual structure work.

Crystals in thermodynamic equilibrium at finite temperature exhibit deviations from ideal periodicity, which are called “thermodynamic defects” (“Eigen-defects”). The various types of thermodynamic defects are discussed and their concentration for thermodynamic equilibrium statet. According to the various types of feed-back among the defects (cooperativity of thermodynamic disorder) with a variation of temperature the thermodynamic disorder may cause phase transitions of first or higher order.

Spheres of transparent single crystals can be oriented on a two-circle, optical goniometer with polarisation setup, using a combination of lenses for conoscopic observations. The method described can be used for tetragonal, hexagonal and orthorhombic crystals, in some favourable cases also for monoclinic crystals but not for triclinic ones, since there the optical axes do not coincide with the crystallographic axes. The accuracy of adjustment which can be reached, is between 30′ and 1°. After the optical preadjustment of spheres, their final adjustment on x-ray diffractometers can be easily made.

The design, construction and performance of an apparatus for high-temperature single-crystal x-ray studies are described. The apparatus has been used successfully on standard Weissenberg and precession cameras. The temperature varied by less than ± 3°C at temperatures up to 900°C during long periods of time.

The symmetry operations of a circular cylinder have been studied by unrolling the cylinder into a plane. All possible classes and their symmetries are given. The seventy-five cylinder groups and, as extreme cases, the groups with infinite-fold cylinder axis and those with an infinite screw pitch are derived and illustrated.

A comparison of the beta synthesis of R amachandran and R aman (1959) with the usual heavy-atom synthesis is made in the case of a three-dimensional structure determination of l -arginine monohydrobromide monohydrate and theoretical results are verified. As predicted by the theory, the beta synthesis reveals the unknown part of the structure with relatively much higher strength than the heavy-atom synthesis.

The crystal structure of gratonite has been redetermined with the use of three-dimensional intensity data. The intensities were obtained by counter and photographic technique. Three chemical units of Pb 9 As 4 S 15 are contained in the unit cell of the symmetry C 3 v 5 – R 3 m with a hex = 17.758 ± 0.014 Å, c hex = 7.807 ± 0.006 Å. The refinement of the structure was performed by the three-dimensional least-squares method. Two independent Pb atoms are surrounded by seven S atoms. As atoms have a trigonal-pyramidal coordination by S atoms. The AsS 3 pyramides are isolated. The As–S distances ranging from 2.234 Å to 2.299 Å are in good agreement with the As–S covalent-bond length. The Pb–S distances obtained are between 2.776 and 3.436 Å.

The crystal structure of l -valine hydrochloride monohydrate, C 5 NO 2 H 11 · HCl · H 2 O has been established using three-dimensional data. The crystals are orthorhombic with space group P 2 1 2 1 2 1 and a = 6.85, b = 21.22 and c = 6.17 Å. The final R value for observed reflections alone is 0.110; including the unobserved reflections, it is 0.135. A brief discussion of the conformation of the molecule is presented. The structure is stabilized by a three-dimensional network of hydrogen bonds.

The crystal structure of the synthetic zeolite, Linde L, K 6 Na 3 Al 9 Si 27 O 72 · 21 H 2 O, has been determined from powder data at room temperature. The zeolite is hexagonal with unit-cell dimensions a = 18.4 Å and c = 7.5 Å. The structure has been refined assuming space group P 6/ mmm . The aluminosilicate framework is based upon the polyhedral cages which are formed by five six-membered and six four-membered rings and are found in canerinite, erionite and offretite. These cavities are linked through the planes of their upper and lower six-membered ring, thus forming columns in which hexagonal prisms and polyhedra alternate, and which run parallel to the c axis. Each column is crosslinked to three others by single oxygen bridges which form part of planar twelve-membered rings circumscribing wide channels parallel to c . Each channel can be represented as a succession of sections, circumscribed top and bottom by twelve-membered rings shared with upper and lower adjacent sections. The rings have free diameters of 7.1 to 7.8 Å. Four cation positions were found, three of which are outside the main channels and closely surrounded by framework oxygen atoms. The fourth position is in the widest part of the main channel close to the channel wall. The water molecules filling the wide channels are only loosely bound to the framework and appear to have only partial regularity of arrangement. Structures have also been developed for a considerable number of so far unknown zeolites with similarities to zeolite L. All these structures can be allocated to the chabazite family, which however on account of its size and structural variety can be divided into four subgroups.

β chloroethyl triptycene, C 22 H 17 Cl, crystallizes with two molecules per asymmetric imit in space group P 2 1 / c with a = 15.99 Å, b = 15.46 Å, c = 16.48 Å, and β = 126°42′. The triptycene nucleus has an approximate three-fold axis of symmetry. The chloroethyl chain lies nearly in the plane of one of the phenyl groups and is oriented in the trans conformation with respect to that phenyl group. The three phenyl groups in each molecule have normal C–C bond lengths near 1.39 Å, while the apical bonds in the eight-membered cage have an average length of 1.53 Å. The apical angles in the cage are near 105° while the angles in the cage adjacent to the phenyl groups are near 113°. Phases for the structure determination were obtained directly from the magnitudes of the intensities by the use of the symbolic-addition procedure.

Li 2 ZnCl 4 · 2H 2 O crystallizes from aqueous solutions with unit-cell dimensions a = 10.24 Å, b = 11.98 Å, c = 6.44 Å. The space group is P 2 1 2 1 2 1 with Z = 4. The structure has been determined by two-dimensional Patterson, Fourier and difference Fourier syntheses and refined three-dimensionally by the method of least squares to a final R = 0.049 for 989 independent reflections. Zn is tetrahedrally coordinated by four Cl; the tetrahedra are not directly linked together. The two Li are octahedrally surrounded by four Cl und two H 2 O. These octahedra are rather distorted and connected in a slightly undulated layer arrangement [similarly as e.g. in γ -Al(OH) 3 ] thus forming nearly regular tetrahedral holes between the layers. These interstices are occupied by Zn. Because of their structural positions both H 2 O are supposed to have tetrahedral distributions of charge.

The compound Pt 12 Si 5 has a high-temperature structure which differs somewhat from the structure of Ni 12 P 5 . The room-temperature structure seems to be isotypic with Ni 12 P 5 . The bonding relation is discussed.

Mössbauer hyperfine absorption spectra have been measured for the iron tungstate minerals, wolframite and ferberite. Characteristic spectra with moderately large electric quadrupole splittings and isomer shifts typical of high-spin ferrous iron are observed.

All 20 components of the piezooptic tensor of taurine were determined from static measurements by a least-square method. The piezooptic properties exhibit a close correlation to the elastic behaviour.